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(a) Consider the additive model Xt = m + Yt with cubic trend mt= Bo + B₁t+ ß₂t² + B3t³. (i) Show that Vmt is a polynomial of degree 2, i.e., a quadratic function. (ii) What is Vmt? Show your reasoning. (b) Exponential smoothing is defined by the following recursion: m₁ = X₁, mt = aXt+ (1 - a)mt-1, t=2,..., n. Suppose we have time series data {7, 4, 1, 3, 8, 11, 11} with X₁ = 7, X₂ = 4 and so on until X7 = 11. Assume that a = 0.6. Calculate me using exponential smoothing.

(a) Consider the additive model Xt = m + Yt with cubic trend mt= Bo + B₁t+ ß₂t² + B3t³. (i) Show that Vmt is a polynomial of degree 2, i.e., a quadratic function. (ii) What is Vmt? Show your reasoning. (b) Exponential smoothing is defined by the following recursion: m₁ = X₁, mt = aXt+ (1 - a)mt-1, t=2,..., n. Suppose we have time series data {7, 4, 1, 3, 8, 11, 11} with X₁ = 7, X₂ = 4 and so on until X7 = 11. Assume that a = 0.6. Calculate me using exponential smoothing.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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(a) Consider the additive model Xt = m + Yt with cubic trend mt= Bo + B₁t+ ß₂t² + B3t³. (i) Show that Vmt is a polynomial of degree 2, i.e., a quadratic function. (ii) What is Vmt? Show your reasoning. (b) Exponential smoothing is defined by the following recursion: m₁ = X₁, mt = aXt + (1 − a)mt-1, t=2,..., n. Suppose we have time series data {7, 4, 1, 3, 8, 11, 11} with X₁ = 7, X₂ on until X7 11. Assume that a = 0.6. Calculate me using exponential smoothing. = = 4 and so
Transcribed Image Text:(a) Consider the additive model Xt = m + Yt with cubic trend mt= Bo + B₁t+ ß₂t² + B3t³. (i) Show that Vmt is a polynomial of degree 2, i.e., a quadratic function. (ii) What is Vmt? Show your reasoning. (b) Exponential smoothing is defined by the following recursion: m₁ = X₁, mt = aXt + (1 − a)mt-1, t=2,..., n. Suppose we have time series data {7, 4, 1, 3, 8, 11, 11} with X₁ = 7, X₂ on until X7 11. Assume that a = 0.6. Calculate me using exponential smoothing. = = 4 and so
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